Variational aspects of the geodesic problem in sub-Riemannian geometry
| dc.creator | Piccione, Paolo | |
| dc.creator | Tausk, Daniel V. | |
| dc.date | 1999-11-26 | |
| dc.date | 2000-05-23 | |
| dc.date.accessioned | 2026-07-07T05:31:57Z | |
| dc.date.available | 2026-07-07T05:31:57Z | |
| dc.description | We study the local geometry of the space of horizontal curves with endpoints freely varying in two given submanifolds $\mathcal P$ and $\mathcal Q$ of a manifold $\mathcal M$ endowed with a distribution $\mathcal D\subset T\M$. We give a different proof, that holds in a more general context, of a result by Bismut (Large Deviations and the Malliavin Calculus, Birkhauser, 1984) stating that the normal extremizers that are not abnormal are critical points of the sub-Riemannian action functional. We use the Lagrangian multipliers method in a Hilbert manifold setting, which leads to a characterization of the abnormal extremizers (critical points of the endpoint map) as curves where the linear constraint fails to be regular. Finally, we describe a modification of a result by Liu and Sussmann that shows the global distance minimizing property of sufficiently small portions of normal extremizers between a point and a submanifold. | |
| dc.description | LaTeX2e, amsart class, 25 pages Replacement on Jan 5th 2000: added Appendix B Replacement on May 23rd 2000: modified Abstract and Introduction | |
| dc.identifier | https://arxiv.org/abs/math/9911215 | |
| dc.identifier | http://arxiv.org/abs/math/9911215 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/79489 | |
| dc.subject | Differential Geometry | |
| dc.subject | 37J05, 37J50, 37J60, 53C17, 70H03, 70H05 | |
| dc.title | Variational aspects of the geodesic problem in sub-Riemannian geometry | |
| dc.type | text |